 Detection of Trends in Extreme Weather Phenomena Comparing the skill of the Block Maxima and Point Process approaches ASP 2011 Colloquim: Statistical Assessment of Extreme Weather Phenomena under Climate Change Erik Haagenson, Agata Imielska, Sara Rodríguez, Anne Sabourin, Jeremy Weiss

influences.shtml Australian Climate Influences

January to October rainfall in SWWA with centred 15 year moving average. Years shown in red are the five lowest on record. SWWA rainfall decline

Trend in winter anticyclone density

SWWA Precipitation

GENERALIZED EXTREME VALUE DISTRIBUTION ANALYSIS (GEV)  Station 9619   Winter Season (May- October)  Maximum value from each winter obtained and fit to GEV

GENERALIZED EXTREME VALUE DISTRIBUTION ANALYSIS (GEV)  Scale and location parameters fit with a linear trend  The best fit was with a trend in the location parameter only  This information was used to set up our experimental design

Experimental Setup Questions : How to simulate data ? (Given desired GEV parameters for the seasonal maxima) Given simulated data, what kind of experiment should we perform ?

Data Simulation ● Season : n = 184 days. ● Number of wet days over a season : nδ : Poisson ditribution (mean : 84 wet days) ● On wet days : Rainfall X has GPD ditribution : ● Seasonal maximum ● Relation GEV/GPD parameters :

Experimental Design ● Year t, simulated data has seasonal maximum (trend b in the GEV location parameter only) ● Range of tested trends : ● b= ( -0.1, -0.05, -0.02, 0, 0.02, 0.05, 0.1, 0.2 ) ● For each value of b : ● simulate Nsim datasets; fit on each of those: – A Poisson point process model – A block maxima model. ● How many times was the trend detected ?

Results

Next Steps  Expand simulations, test over a series of trends (expand curves)  Develop theoretical approximations to bound the detectability of trends to help guide detection of trends in extreme rainfall

References  Bates, B.C., Hope, P., Ryan, B., Smith, I., Charles, S., Key findings from the Indian Ocean Climate Initiative and their impact on policy development in Australia, Clim. Change, 89: , doi: /s  Bates, B.C., Chandler, R.E., Charles, S.P., Campbell, E.P., Assessment of apparent nonstationarity in time series of annual inflow, daily precipitation, and atmospheric circulation indices: A case study from southwest Western Australia. Water Resources Research, 46: W00H02, doi: /2010WR  Fowler HJ, Wilby RL (2010) Detecting changes in seasonal precipitation extremes using regional climate model projections: Implications for managing fluvial flood risk. Water Resources Research 46:W03535 doi: /2008WR  Hennesy, K.J., Suppiah, R., Page, C.M, Australian rainfall changes, , Aust. Meteor. Mag., 48:1,  Indian Ocean Climate Initiative (IOCI) 2002, Climate Variability and Change in Southwest Western Australia, Dep. Of Environ. Water and Catchment Prot., East Perth, WA, Australia.  Laverty, B.M., Kariko, A.K., Nicholls, N., A high-quality historical rainfall data set for Australia. Aust. Meteor. Mag., 40,  Li Y, Cai W, Campbell EP (2005) Statistical modeling of extreme rainfall in Southwest Western Australia. Journal of Climate 18:  Reyes H., Vaquera H. and Vilaseñor J. Estimation of trends in high urban ozone levels using the quantiles of (GEV), Environmetrics, vol. 21, pp ,  Zhang X, Zwiers FW, Li G (2004) Monte Carlo Experiments on the Detection of Trends in Extreme Values. Journal of Climate 17:

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